Short answers, pulled from the story.
An irregular galaxy is a galaxy that lacks a distinct regular shape, with no nuclear bulge and no spiral arm structure. Irregular galaxies do not fall into any of the standard classes of the Hubble sequence and are often chaotic in appearance.
Irregular galaxies are thought to make up about a quarter of all galaxies. A large portion of the Local Group, the galaxy cluster that includes the Milky Way, consists of irregular galaxies, most of them classified as dwarf irregulars.
The three major types are Irr-I galaxies, which show some structure but not enough for standard classification; Irr-II galaxies, which lack any classifiable structure and are often shaped by collisions; and dwarf irregular galaxies, which fall below a luminosity threshold and closely resemble the earliest galaxies in the universe.
Irregular galaxies lack the density waves present in spiral galaxies, which are believed to contribute to star formation. This makes them ideal environments for studying how stars form without that organizing influence, with gas movement, massive stars, and giant HII regions playing a larger role instead.
The Large Magellanic Cloud was once classified as irregular but has since been reclassified as type SBm, a barred Magellanic spiral. The Small Magellanic Cloud remains classified as an irregular galaxy of type Im, though it does contain a bar structure.
Irregular galaxies can form through several processes: some were once spiral or elliptical galaxies deformed by an uneven external gravitational force; others may be young galaxies that have not yet settled into a stable shape; and some are the result of galaxy collisions or mergers.